Artemis Valanis

School of Rural and Surveying Engineering

Laboratory of Photogrammetry

National Technical University of Athens, Greece

FITTING, PORTRAYAL AND MAPPING FOR THE PRODUCTION OF 2nd ORDER SURFACES PHOTOMOSAICS

GENERAL INFORMATION AND OBJECTIVESThis presentation refers to an extensive study that has

been carried out within the framework of a much greater project. The project was assigned to the Laboratory of Photogrammetry and involved the thorough survey and recording of the world famous Byzantine Daphni Monastery of Athens (11th century).

The main objective of this study was the creation of large-scale (1:5) developments of 2nd-order surfaces.

COURSE OF STUDY

Data collectionSurface fittingReference system definitionCreation of the “Intermediary Model”Choice of the most suitable projection Production of the developed images Creation of the photomosaics

PROBLEMS ENCOUNTERED

- The choice of the most suitable model

- The calculation of the approximate values of the unknowns

- The definition of a new reference system

- The fact that the mathematically defined surface generally differs from the real object surface

DATA USED

Photographs of scale: k= 1:25

Scanning resolution: 600 dpi

Geodetically collected point coordinates

Photo orientations

DEMs

SURFACE FITTING

- Choice of a model

- Calculation of the approximate values of the unknowns

- Creation of the least-squares adjustment programs with computational optimization

- Testing of the programs with simulation data

- Implementation with actual data

REFERENCE SYSTEM DEFINITION

MODEL OR REAL OBJECT SURFACE ?

However, the most important problem encountered was the fact that the mathematically defined surface generally differs from the real object surface.

Thus, in order for the photomosaicking to be possible, the one-to-one correspondence between the points of the real and the model surface had to be ensured. This was achieved with the creation of the “Intermediary Model”, which is based on the DEM of the real surface.

THE PROBLEM CAUSED DUE TO THE DIFFERENCE BETWEEN THE MODEL AND THE REAL SURFACE

(PP)

(Xc,Yc,Zc)

ModelReal Surface

(Ph1)

(Ph2)

ERROR PROPAGATION

Least-squares adjustment

σο dR = 3cm

|dR| 3cm (68%)

|dR| 6cm (95%)

|dR| 9cm (99%)

ERROR PROPAGATION

-15-10

-505

1015

-90 -60 -30 0 30 60 90

Longitude (degrees)

Err

or in

the

x po

sitio

n (c

m)

dR = 3cm dR=6cm dR=9cm

ERROR PROPAGATION

-30

-20

-10

0

10

20

30

-90 -60 -30 0 30 60 90

Latitude (degrees)

Err

or

in the

y p

osi

tion

(cm

)

dR = 3cm dR = 6 cm dR = 9cm

PROJECTION Choice of the most proper projection

Criteria:Suitability for the application

Minimization of the distortions Implementation:

Projection-plane (xp, yp) Sphere “Intermediary Model”

Actual object-surface

Geodetical coordinates

Coordinates on the photographic plane

Acquisition of the colour for the corresponding position (xp, yp) on the projection plane

Developed Image creation

RESULTS- Mollweide Conformal Projection -

RESULTS- Oblique Mercator Projection -

CHARACTERISTICS OF THE METHOD DEVELOPED

Accuracy and reliabilityHigh qualityAbility to work with RGB imagesCapability to incorporate numerous images for a

single objectSuccessful mosaickingProgram performance highly dependent on the

platform and the resources of the system used